Equivariant neural networks for robust $\textit{CP}$ observables

We introduce the usage of equivariant neural networks in the search for violations of the charge-parity ($\textit{CP}$) symmetry in particle interactions at the CERN Large Hadron Collider. We design neural networks that take as inputs kinematic information of recorded events and that transform equivariantly under the a symmetry group related to the $\textit{CP}$ transformation. We show that this algorithm allows to define observables reflecting the properties of the $\textit{CP}$ symmetry, showcasing its performance in several reference processes in top quark and electroweak physics. Imposing equivariance as an inductive bias in the algorithm improves the numerical convergence properties with respect to other methods that do not rely on equivariance and allows to construct optimal observables that significantly improve the state-of-the-art methodology in the searches considered.